Abstract
We use the covariant harmonic-oscillator wave functions to formulate the vacuum quark-pair-creation model of three-meson vertices and meson-decay matrix elements. It is pointed out first that the harmonic-oscillator wave functions can be given a covariant probability interpretation. We then use this probability concept to construct the three-meson vertex function. Using a relativistic $L\ensuremath{-}S$ coupling scheme, we calculate the decay amplitudes for the $B\ensuremath{\rightarrow}\ensuremath{\omega}\ensuremath{\pi}$ and ${A}_{1}\ensuremath{\rightarrow}\ensuremath{\rho}\ensuremath{\pi}$ decays. For the $B$ decay, the calculated polarization ratio turns out be in excellent agreement with the experimental value. For the ${A}_{1}$ decay, the calculated ratio is consistent with the present experimental value. We have also calculated the decay ratio for the well-established $\ensuremath{\rho}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}$ and ${A}_{2}\ensuremath{\rightarrow}\ensuremath{\rho}\ensuremath{\pi}$ decays. It is shown that the harmonic-oscillator wave functions produce a number which is very close to the experimental value. The limitations of the $L\ensuremath{-}S$ coupling scheme are discussed.
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